All US immigrant visa applications require police reports. (this includes 'K' visa applicants) You must provide a police report from each locality within your country of nationality in which you lived for 6 months or more after the age of 16. If you have lived only in the UK, one national police certificate is sufficient for all UK localities.
You must also provide a police report from any country you lived in for 12 months or more after the age of 16.
If you are already in the USA and doing an adjustment of status (AOS), you do not need a police report from anywhere. USCIS will run their own checks on you. Similarly, if you are applying from abroad and have lived in the US for 12 months or more after your 16th birthday you do not need to provide a US police certificate.
Requesting Police Reports
The US Department of State maintains a Reciprocity Schedule for most countries. You can use this to find out if a document is available to you, and how to order it.
After selecting your country of choice and jumping to that page, scroll past the visa fee schedule to find the civil document information. Information on how to obtain police certificates for that country is listed under the heading Police Records. Some countries have more than one kind of police certificate. You must read this section carefully and ensure you request the correct one. For the United Kingdom the correct document is called the 'ACPO'.
Information from the Department of State Website
The relevant page on the US Department of State website is here:
Please read this link in it's entirety before posting any questions on the forum.
If a report comes back with anything other than all clear then you will probably need the court records/outcome of the case documented in addition to the Police Certificate.
Any arrests must be declared in your application even if your Police Certificate comes back 'clean' or your record was expunged or equivalent.
Do I need a police certificate if I am traveling to the US on the Visa Waiver Program? No, you do not.
If my police report comes back 'clean' does that mean I don't have to declare my convictions? No, you still must list any convictions.
My police report is not clean, will I get a visa? It depends on the crime.